Force-history dependence and cyclic mechanical reinforcement of actin filaments at the single molecular level

In the physiological environment, biomolecular bonds within the actin cytoskeleton and adhesion complexes experience dynamic mechanical forces over time (Schwartz, 2009; Parsons et al., 2010). The actin cytoskeleton is a primary force-bearing structure and, thus, critical to a variety of cellular functions such as migration, control and maintenance of morphology, and differentiation (Watanabe and Mitchison, 2002; Pollard and Cooper, 2009; Pollard and Borisy, 2003; Discher et al., 2009). Under physiological conditions, actin monomers (G-actin) spontaneously polymerize into a double-helical actin filament (F-actin). Initiation of actin polymerization, assembly and/or turnover of F-actin, and crosslinking into networks are regulated by a number of actin-binding proteins (dos Remedios et al., 2003; Pollard, 2016). The actin filament has two ends, the pointed and barbed ends, each of which has distinct properties that result in clear polarity. The pointed end, known as a slow-growing end, has slower polymerization and depolymerization rates than the barbed end, the fast-growing end (Pollard, 1986; Kondo and Ishiwata, 1976). Mechanical stimuli, either externally from the microenvironment or internally by actomyosin contraction, are key factors regulating the dynamic cytoskeletal rearrangement and cellular function (Orr et al., 2006). However, mechanisms underlying the mechanotransduction and force regulation of actin cytoskeleton dynamics still need to be elucidated.

Actins sense forces. Tension on F-actin changes its mechanical properties and induces changes in binding affinities of actin­-binding proteins (Fujime and Ishiwata, 1971; Isambert et al., 1995; Yasuda et al., 1996; Matsushita et al., 2011; Shimozawa and Ishiwata, 2009). Molecular dynamics studies have demonstrated that tensile forces applied to F-actin decreased its twist angle and the structural changes led to an increase of extensional and torsional stiffness (Matsushita et al., 2011). Force-dependent distortion of F-actin under tensile force was measured using optical tweezers (Shimozawa and Ishiwata, 2009). The structural distortion led to inhibition of cofilin binding to F-actin, after which the fiber disassembly was significantly delayed compared to unloaded F-actin (Hayakawa et al., 2011). Another case of tension-dependent affinity of actin binding proteins is myosin, with the stretched F-actin showing higher affinity for the myosin II motor domain (Uyeda et al., 2011). Interestingly, constant tensile force on F-actin also affects its own depolymerization kinetics (Lee et al., 2013), suggesting that mechano-chemical coupling in actin dynamics is essential for its cellular functions.

Intuitively, bonds in biological interactions would be slip bonds, in which bond lifetime decreases as tensile force increases. Slip bond behavior has been observed in most biomolecular interactions (Merkel et al., 1999; Fritz et al., 1998). By contrast, catch bonds show a counterintuitive behavior where bond lifetimes increase as tensile force increases up to a threshold point. This has been observed in several non-covalent interactions of intracellular and extracellular molecules, such as myosin and actin (Guo and Guilford, 2006), integrin and fibronectin (Kong et al., 2009), P-selectin and PSGL-1 (also known as SELPLG) (Marshall et al., 2003), and L-selectin and PSGL-1 (Sarangapani et al., 2004). Several mechanisms have been proposed to explain the catch bond, such as allosteric, sliding-rebinding, or multi-state models (Lou and Zhu, 2007). Using atomic force microscopy (AFM) Lee et al. (2013) demonstrated that the kinetics of actin depolymerization are also force-dependent, biphasic catch–slip bonds. Bond lifetimes of G-actin–G-actin (GG) and G-actin–F-actin (GF) interactions were prolonged as the applied tensile force increased and then shortened beyond a threshold.

Mechanical reinforcement has been observed in cell matrix-adhesive interactions. Catch bonds formed between FimH and mannose demonstrated enhanced bond strength after mechanical preconditioning (Yakovenko et al., 2008), and preconditioning by cyclic tensile forces prolonged bond lifetimes of integrin α₅β₁ and fibronectin interaction by switching bond states from short-lived to long-lived (Kong et al., 2013). This phenomenon was termed cyclic mechanical reinforcement, and suggests that the history of force loading on biomolecular bonds could be a critical regulator of interaction kinetics.

These previous studies gave rise to two questions: does the force-induced strengthening of actin bonds last after the force is reduced, and does the history of force loading on actin bonds affect the depolymerization kinetics? To address these questions we investigated actin depolymerization kinetics under a range of dynamic force conditions at the single molecular level using AFM (Fig. 1A,B). This study provides insight into how actin dissociation kinetics is regulated by dynamic tensile forces, which are closer to physiological conditions than constant force loading.

Under linearly clamped tensile forces (i.e. without mechanical preconditioning; Fig. 1C, left), average bond lifetimes of GF interactions increase from ∼0.3 s to ∼0.9 s as the clamping force increases to 20 pN, and then the lifetimes decreased as force further increased (Fig. S1A). We asked whether the enhanced actin–actin interactions under high tensile forces (15–30 pN) persist or revert immediately to those with short lifetimes when the loaded force is released. Therefore, we imposed a single cycle of tensile forces on actin bonds with different magnitudes of peak forces to examine the effect of mechanical preconditioning with high forces. Throughout this study, F-actin was polymerized over 1 h, and so all actin subunits should have been converted into ADP-actin. Experiments were performed in the presence of 1 mM ATP, which should allow nucleotide exchange of G-actin on the AFM probes to regenerate ATP-G-actin. The middle panel of Fig. 1C is a representative force–time trace of mechanical preconditioning by a single high peak force: the sequence is loading peak force, unloading to low force and then clamping for measurement of the bond lifetime. The GF bonds were loaded to peak forces (15–27 pN) and reduced to low force (8–10 pN) for clamping.

Interestingly, when the loaded peak forces were lowered, bond lifetimes were significantly prolonged instead of immediately reversing to short lifetimes or rupturing, and the average lifetimes increased even further as the peak force increased (Fig. 2A). The average lifetime increased up to 9.1 s with 27 pN of peak force; this is more than 30-fold reinforcement compared to that without mechanical preconditioning. Bond survival probability, which is the natural log of the total number of events with a lifetime longer than t normalized by the natural log of total number of events, is plotted versus bond lifetime (Fig. 2B). The lifetime at ∼10 pN without mechanical preconditioning (notated as 10 pN in Fig. 2A and ‘no peak force’ in Fig. 2B) exhibited a single exponential distribution, indicating a first-order dissociation of GF bonds (green squares in Fig. 2B). Peak force preconditioning shifted the lifetime distributions toward longer lifetimes and yielded multi-exponential decay, suggesting multiple-state dissociation. A negative control was conducted by preparing actin on the substrate of the Petri dish and streptavidin (SA) on the cantilever tip. The binding frequency was ∼3%, which was in the range of a typical non-specific binding (data not shown).

The significant bond reinforcement with high peak force preconditioning led us to question whether low peak force (∼10 pN), which induced short lifetimes (∼0.3 s) under a linear clamping mode, is also able to modulate actin interactions when it is repetitively applied. Thus, multi-cyclic tensile forces with a 10 pN peak were tested. The right-hand panel of Fig. 1C is a representative force–time trace of sequence of loading and unloading with 1.5 cycles on the bond. Multi-cyclic loading of a low peak also significantly prolonged the bond lifetimes up to 20-fold and yielded multi-state lifetime distributions (Fig. 2C,D). The post-preconditioning lifetime distributions were shifted to the right and showed multi-state dissociation. The values noted as 0.5 cycle in the figure indicate measurements at 10 pN of linearly clamping without mechanical preconditioning for comparison.

We tested to find goodness-of-fit among the single-, two-, and three-state dissociation models. The lifetime distributions were best fitted by a two-state dissociation model. The two states could be interpreted as short- and long-lived population (details in Materials and Methods). The values of fraction of the long-lived state were about half (0.4–0.6) in both cases (Fig. S2A,C). The reciprocal off-rate of the long-lived state, a theoretical mean lifetime, increased as the peak force increased (Fig. S2B) and slightly increased as number of repetitive cycles increased (Fig. S2D).

These results demonstrated that the actin bonds enhanced by high tensile force are not only retained, but much further reinforced after the force is released. In addition, repetitive tensile loading of low force was also able to significantly reinforce the GF interactions. It could result from switching the short-lived to the long-lived state in the homogeneous population of GF bonds or from polarity of dissociation kinetics at the two ends of F-actin, the barbed and pointed ends. Therefore, we further investigated the possibility of polarity in dissociation kinetics at the barbed and pointed ends under the same dynamic force loading conditions.

The two ends of F-actin were distinguished by adding capping proteins, CAPZ to cap the barbed end and TMOD3 for the pointed end, as described previously (Lee et al., 2013). The effect of the magnitude of peak force preconditioning was examined by the same time–force path as described above, loading the GF bond with high peak forces (15–30 pN), then reducing the force to a low range (8–10 pN) to measure the bond lifetime (Fig. 1C, middle). In the low force range of 8–10 pN, we detected bond lifetimes of ∼0.30 s at the barbed end and ∼0.35 s at the pointed end with no statistical significance (Fig. 3A,C). However, in our previous study (Lee et al., 2013), we reported bond lifetimes of 0.35–0.45 s at the barbed end and 0.5–0.6 s at the pointed end with a significant difference. The reason for this discrepancy is unknown (see Discussion).

At both the pointed (Fig. 3A,B) and barbed ends (Fig. 3C,D), the post-conditioning average bond lifetimes were significantly prolonged as compared to when those are measured without any mechanical preconditioning, and the lifetimes further increased as the peak force increased. The averaged bond lifetimes were not reverted to short (0.3 s) nor maintained at the maximum (0.9 s) when force was clamped at the low range following a high peak force. But the lifetimes were significantly prolonged: at the pointed end, to 3.9 s (13-fold compared to linear clamping) with 16 pN-peak, 8.8 s with 21 pN-peak, and 9.0 s with 26 pN-peak (Fig. 3A,B); and at the barbed end, the lifetimes were prolonged to 1.9 s with 15 pN-peak, 3.6 s with 22 pN-peak and 5.5 s with 27 pN-peak (Fig. 3C,D). The kinetic polarity between the pointed and barbed end was clearly observed and it was plotted as the difference in the average lifetime at both ends versus the preconditioned peak force (Fig. 3E). Adding capping proteins, TMOD3 and CAPZ, decreased adhesion frequencies from 22% to 12.5% and 8.7% in the presence of TMOD3 and CAPZ, respectively.

The lifetime distributions exhibited multi-state dissociation kinetics at both ends. We tested to find goodness-of-fit and the best-fit off-rates and occupancies are summarized in Table S3 and Fig. S3. Under this mechanical preconditioning, lifetime distributions of the pointed and barbed end were best fitted with the two-state dissociation model (Fig. S3). The fractions of the long-lived population and the values of reciprocal of k_{off_L} were larger at the pointed end compared to those at the barbed end. This indicates that more bonds were converted to the long-lived state from intrinsic short-lived state, and that the high force-induced bond tends to live longer at the pointed end as compared to the barbed end.

The effect of repetition of mechanical preconditioning with a low peak force (∼10 pN) was also examined (Fig. 1C, right) at the pointed and barbed ends as described above. Similar reinforcement features were observed at both ends (Fig. 4). At the pointed end, the post-conditioning bond lifetimes were significantly enhanced to 3 s (10-fold) after 1.5 cycles, 4.8 s (16-fold) after 2.5 cycles and 6.3 s (21-fold) after 3.5 loading cycles, and increasing the number of cycles further prolonged the average bond lifetimes (Fig. 4A,B). At the barbed end, the post-conditioning lifetimes were also significantly prolonged after 1.5 cycles (Fig. 4C,D); however, increasing the number of cycles did not further increase the average lifetimes. The difference in the average bond lifetime at both ends was plotted as a function of the number of cycles (Fig. 4E). Similar to the peak force preconditioning, the multi-cycle preconditioning effect was significantly suppressed at the barbed end and the cumulative effect of cycles was also diminished as compared to the reinforcement that was observed at the pointed end. In addition, the lifetimes of the two ends were shorter than those preconditioned with high peak forces. The zero value at 0.5 cycle in Fig. 4E indicates no differences in average lifetime when GF bonds were linearly clamping at 10 pN. No difference was observed with 1.5 cycles; however, when the number of repetition increased to 2.5 and 3.5 cycles, the polarity of dissociation kinetics emerged.

At both ends, repetitive cyclic preconditioning also yielded multi-state lifetime distributions. We tested to find that goodness-of-fit and lifetime distributions at the barbed end were fitted best by the two-state model, and distributions at the pointed end were best fitted by the three-state dissociation model, but the two-state model was not rejected by the extra sum-of-squares F test. (Table S3).

These data demonstrated that (1) cyclic mechanical preconditioning induces significant reinforcement in bond lifetimes of GF interactions at the pointed and barbed ends, (2) the different tensile loading conditions result in different dissociation kinetics, and (3) the two ends show a difference in the force-modulated dissociation kinetics. The actin bond at the end of F-actin consists of two interactions of terminal subunits, intra-strand and inter-strand contact of GG, and these two bonds are involved in dissociation of the GF bond (Holmes et al., 1990). Therefore, we further investigated how the same force-loading paths imposed on F-actin affect dissociation kinetics of GG bonds.

Under linearly clamped tensile forces (Fig. 1C, left), average bond lifetime of GG interaction increased from 0.3 s to 0.6 s as the force increased from 5 pN to 11 pN, and the lifetime decreased as force further increased (Fig. S1B). Compared to the GF interaction, bond lifetimes were shorter and the effective range of force was narrower in the GG interaction. Thus, we adjusted the force range for peak force experiments. The same force–time paths were applied to the GG bond to examine the effect of cyclic mechanical preconditioning on the G-actin dimer dissociation. A high range of peak forces for GG bond, 10–20 pN, were loaded to examine whether the induced high affinity can remain when the force is reduced to a low force, 5 pN, which induce a low affinity state when it was linearly clamped without preconditioning. Unlike GF interactions, the GG bond lifetime reached a maximum at 10–11 pN. However the same multi-cycle with 10 pN peak force was loaded to observe GG interaction under the same mechanical conditions used earlier in order to relate to the force-modulated GF behavior.

The behavior of GG interaction under cyclic mechanical preconditioning was qualitatively similar to that of GF. After peak force preconditioning, average lifetimes did not revert to short or maintain the maximum (0.6 s), but were significantly prolonged. Also, as the peak force increased, the average lifetime further increased (Fig. 5A): 2.5 s (8-fold) with 10 pN-peak, 5.2 s (17-fold) with 15 pN-peak, and 5.5 s (18-fold) with 20 pN-peak. GG lifetimes obtained under linear clamping were distributed as a single-exponential decay and it suggests a homogeneous first-order dissociation of the bond (Fig. S4A,D, green squares). Similar to the GF interaction, the post-preconditioning lifetime was distributed as multi-exponential decays. The fractions of long-lived state were about half, and the reciprocal of k_{off_L} increased as the peak force increased (Fig. S4B,C).

The repetitive-cyclic preconditioning also significantly prolonged the average lifetimes about 3-fold; however, increasing of the number of cycles did not further enhance the average lifetime and the lifetimes were much shorter than those preconditioned with peak forces (Fig. 5B; Fig. S4D). The lifetime distributions were fitted best by a two-state dissociation model. The values of long-lived state fraction indicate that about half the GG interactions were switched to the long-lived state (Fig. S4E,F).

Overall GG interactions with cyclic mechanical preconditioning were qualitatively similar to the GF interactions: significantly prolonged GG bond lifetimes, force-history dependence, and multi-state dissociation.

Our study is the first to demonstrate force-history dependence, cyclic mechanical reinforcement, and polarity of force-dependent actin depolymerization at distinct ends of F-actin at the single molecular level using AFM, although some technical limitations remain to be considered (see below). The cyclic mechanical reinforcement has been observed in different scales of actin cytoskeletal structures: mechanical hardening of actin-α-actinin meshes by cyclic shearing (Schmoller et al., 2010), and local mechanical stiffening induced by local cyclic stretching and/or compression on the surface of the fibroblast (Watanabe-Nakayama et al., 2011). Under physiological conditions, transmitted dynamic external forces and actomyosin contraction may act as cyclic mechanical preconditioning and induce force-history dependent reinforcement of F-actin. The reinforced actin filament may help to establish stable networks and integrin-mediated adhesion by lasting longer, thus allowing more time for transmission of the force and recruitment of focal adhesion proteins such as vinculin (Grashoff et al., 2010). The differential force-modulated depolymerization kinetics at the two filament ends could be a mechanism to regulate cytoskeletal rearrangement acting as a force sensor.

Compared to linear clamping at a given force (Fig. 1C, left), dynamic tensile preconditioning (Fig. 1C, middle and right) revealed additional features of actin dissociation kinetics. Interestingly, under linearly clamped tension, GF interactions at both ends exhibited qualitatively and quantitatively similar catch–slip bonds (Lee et al., 2013), whereas under the dynamic force loading the actin interactions formed significantly more stable, but different, bonds at each end. That is, kinetic polarity was observed as the mechanical reinforcement was significantly more effective at the pointed end compared to that at the barbed end. Structural polarity was newly observed in the updated Oda F-actin model (Narita et al., 2011). The structure of the barbed end was the same as that in the middle of the filament as can be expected, whereas the structure of the pointed end differs from the barbed end. The terminal actin subunit at the pointed end is tilted further to the penultimate subunit than at the barbed end. This allows the two end subunits to form a tighter loop-to-loop interaction, which is not structurally possible at the barbed end. It suggests that the extra loop-to-loop inter-strand interaction inhibits association of another G-actin monomer and also builds a higher kinetic barrier for monomer dissociation at the pointed end, resulting in the intrinsic slower actin dynamics than those at the barbed end (Pollard, 1986). The SMD simulation also showed that new actin–actin interactions were formed by pulling differently at the barbed and pointed ends (Lee et al., 2013). Together, the intrinsic structural polarity might induce the kinetic polarity under cyclic force loading.

The force-induced multi-state dissociation model has been introduced in biomolecular interactions, such as a two-state model for α5β1 integrin and its ligands under mechanical preconditioning (Kong et al., 2013) and a three-state model for LFA-1 and/or ICAM-1 catch bonds (Chen et al., 2010). The three states were interpreted as short-, intermediate- and long-lived populations. Their study suggested that the force induced intermediate- and long-lived states and the three states co-exist in dynamic equilibrium. In these GF interactions, multi-populations of the bond state were observed after distinguishing the barbed and pointed ends (Figs 3 and 4), indicating that the population of long-lived state was induced by cyclic tensile preconditioning. The two-state dissociation model was preferred over single- or three-state, except for the precondition of repetitive cycles with a low peak force at the pointed end. The three-state model was preferred for those conditions at the pointed end but the two-state model was not rejected, indicating that the two-state dissociation model still is reliable to use to explain the distribution. The calculated parameters from the two-state model, long- and short-lived fraction and k_off, are very useful to understand the curves. Therefore, we used the two-state dissociation model to interpret our data (Table S3). The obtained k_off values of short-lived states are comparable to those of Fujiwara et al. (2007).

There are several models to explain force-dependent molecular interactions. The sliding-rebinding model has been proposed as a structural mechanism underlying other catch bonds of different biomolecular interactions, such as actin–actin (Lee et al., 2013), P-selectin–PSGL-1 (Lou and Zhu, 2007), L-selectin–PSGL-1 (Lou et al., 2006) and GPIbα–VWF (Yago et al., 2008). Two G-actin subunits interact with each other by intra-strand (long-pitch, parallel) or inter-strand (short-pitch, anti-parallel) contact, and both types of contact are involved in depolymerization of the terminal subunit at the tip of F-actin (Holmes et al., 1990); the former is the case for GG interaction, and the latter is for GF interaction in this study. Steered molecular dynamics (SMD) simulation based on Oda's F-actin model (Oda et al., 2009) demonstrated that pulling causes relative sliding, which induces newly formed salt bridges between actin subunits in the dimer or at the end of F-actin (Lee et al., 2013). The force-induced strong interactions might be important in the catch bond behavior. Similar to this, in our case, pulling by cyclic tensile loading might induce strong inter-contacts between GG dimers or end subunits of F-actin. However, cyclic mechanical reinforcement is significantly more effective in lengthening bond lifetime than the catch bond induced by linear clamping, suggesting that the procedure of force release, followed by pulling, might induce newly formed and more stable interactions between actin subunits, resulting in further reinforcement of the bonds.

Under the low force range, bond lifetimes of GF interaction were not significantly different at the barbed end (0.30 s) and at the pointed end (0.35 s) in this study, which was inconsistent with our previous report (0.35–0.45 s at the barbed end and 0.5–0.6 s at the pointed end) (Lee et al., 2013). Such inconsistency might be caused by technical variations because these experiments were performed by different researchers at room temperature without precise temperature control. Mechanistically, these technical variations may affect the states of actin-bound nucleotides that strongly influence the off rates of actin monomers from filament ends (Korn et al., 1987; Pollard, 1986; Fujiwara et al., 2007). Dissociation rates of ATP-actin are only modestly different at the barbed end (1.4 s⁻¹) and the pointed end (0.8 s⁻¹). However, ATP hydrolysis, which is enhanced upon polymerization, and subsequent release of phosphate alter the dissociation rates and magnify the kinetic differences at the two ends (Korn et al., 1987; Pollard, 1986; Fujiwara et al., 2007; Jégou et al., 2011). To clarify the effects of nucleotide states, experiments using actin bound to ADP or AMP-PNP (a non-hydrolyzable ATP analog) and experiments in the presence of inorganic phosphate to generate ADP-P_i-actin will be required. Furthermore, whether nucleotide states of actin are involved in cyclic reinforcement of actin is an important question to be tested in the future.

We assumed that interactions between G-actin on the cantilever and the end of F-actin on the Petri-dish would be dominant in GF experiments, because of the surface treatment with BSA, the biotin in the working solution, the adjusted density of immobilized actin and the washing steps. However, some unusual interactions, like interactions between G-actin and the side of F-actin, may still have occurred. The fraction of the specific (interactions between actins) but not expected (monomer dissociation from the end of the tip) interactions should have been low enough not to affect overall force-dependent characteristics of GF interactions. Binding of capping proteins, CAPZ and TMOD3, could also have affected the force-dependent behavior. Capping the end of F-actin might alter mechanical and/or biochemical properties of F-actin and could result in modulating the response of F-actin to the mechanical preconditioning.

Multiple bond formation occurs during interactions and can be modulated by different experimental parameters and sample preparations. Typically, adhesion frequency increases as contact time (the duration of contact between cantilever and the surface) increases, and reaches a plateau after a certain contact time. Increase in adhesion frequency could be related to multiple bond formations. Higher molecular density yields higher adhesion frequency and increases the chances to form multiple interactions. This AFM has been set up to dominantly observe single molecular interactions by adjusting contact time between two surfaces (molecules) and coating concentration of immobilized actins (details in Materials and Methods) (Chesla et al., 1998; Kong et al., 2013; Lee et al., 2013). Rupture curves of binding interactions were monitored with 1 ms of time resolution. Multiple ruptures (stepwise rupture instead of clear single drop), indicating multiple bonds, were removed from the data set. As long as the ruptures do not happen at the same time, multiple rupture is easily detected with 1 ms resolution.

In our experiments, 2 µM TMOD3 was used, which we assume causes TMOD3 to be substantially in excess of actin pointed ends. Exact concentrations of actin pointed ends were difficult to estimate because the lengths of F-actin were not controlled and F-actin was immobilized to the surface. Nonetheless, we estimate that ∼90% of actin pointed ends are capped by TMOD3 based on the published K_d (0.17 µM) for binding of TMOD3 to actin pointed ends (Fischer et al., 2003) and assumed concentrations of actin pointed ends in a range of 10–100 µM.

Force-clamped experiments potentially have issues with selection bias. The bond needs to survive until it is clamped and measured. Survival rates (the rate of bonds surviving until clamping at a given force over completed adhesions) vary depending on clamping forces; as force increases survival rate tends to be lower. It is possible that stronger bonds were chosen during the preconditioning process with high forces (20–30 pN). The selection bias would be very minimal in the repetitive reinforcement experiments, which were loaded with low forces (∼10 pN) in GF interactions. In contrast, the selection bias would be critical in the analysis of GG interactions. Actin dimers are highly unstable with dissociation rates in the orders of 10⁸–10¹⁰ s⁻¹ (Sept and McCammon, 2001). If all actin dimers dissociate at these rates, such GG interactions would not survive for AFM measurements and could not be distinguished from non-specific probe interactions. Given that the bond formation was specifically detected upon coating with G-actin, which could be inhibited by latrunculin A (Lee et al., 2013), we hypothesize that a minor population of actin dimers could survive for a prolonged period and be selectively detected in our studies. The biophysical nature of such long-lived actin dimers remains unknown. A previous study predicted the presence of ‘activated actin monomers’ preceding the nucleation process during actin polymerization (Cooper et al., 1983), which might be related to the formation of such long-lived actin dimers. Additional biophysical studies of actin dimers in the presence or absence of force may provide insight in the heterogeneity of actin dimers.

In addition to selection bias, the conditions of molecular immobilization on surfaces might have affected the dissociation rates. The slow dissociation rates of G-actin–G-actin interactions have been observed consistently in our experimental setup (this study and Lee et al., 2013). Actin was immobilized on the surface via biotin-streptavidin, which prohibited actin diffusion and limited freedom in the movement of actin molecules. Such physical limitations and/or covalent biotinylation might have affected conformation and other biophysical properties of actin.

With our results taken together, we propose a force-dependent actin dissociation model (Fig. 6). In this kinetic model, force (f) is added as a governing parameter. The dynamics between the short-lived and long-lived states is regulated by force-loading history [f(t)], with different force-loading therefore resulting in different sizes of the long-lived population [w(f(t))] and interaction kinetics [K_{D_L}(f(t))]. Without force loading, the value of w is zero. In the case of GG interactions, there is one more possible explanation for the half fraction of the long-lived state apart from switching of the short-lived to the long-lived state in the homogeneous population of GG bonds. It could result from intra- or inter-strand bond formation, which would exhibit different bond states after dynamic force loading. A combination of the two possibilities would cause the generation of the two populations, with each about the same size.

Our data demonstrate that the force-history dependent mechanical reinforcement and polarity of dissociation kinetics are possible mechanotransduction mechanisms, which involve force regulation of actin cytoskeletal dynamics and depolymerization kinetics. Further investigations of the mechanochemical coupling of actin-binding proteins to modulation of actin cytoskeletal dynamics need to be completed under dynamic force loading conditions at the single molecular complex level.

A custom-made AFM (Fig. 1A) and force-clamped experimental procedures were used as previously described (Kong et al., 2013; Lee et al., 2013). The AFM experiments were designed to investigate G-actin dissociation of the dimer and at the ends of F-actin. Briefly, the AFM consisted of a laser (Oz Optics, Canada), photodiode, tip mount and a piezoelectric translator (PZT; Physik Instruments, Germany). The laser was focused on the back of the cantilever end (Bruker, USA), mounted on the PZT and detected by a photodiode to measure cantilever deflection. The PZT and tip mount were integrated with a capacitive feedback sensor to control the distance between the tip and the surface of the Petri dish. The cantilever deflection (volts) was converted to the magnitude of the force (newtons), bending the cantilever according to the spring constants (1.5–10 pN/nm) of the cantilevers employed. Cantilever spring constants were calibrated for each experiment in situ using thermal fluctuation analysis. A personal computer with a data acquisition board (PCI-MIO-16XE-10, National Instruments, USA) controlled the PZT and received the signal input from the photodiode. Labview (National Instruments, USA) was used as the interface between the user and the data acquisition board. The maximum measurement for lifetime was 50 s. Some variation of measured forces between studies might have occurred as a result of differences in the spring constant of cantilever tip (measured from thermal fluctuation), force-base line determination, etc. For example, the measurement variation of the spring constant could be up to ∼20% (Lévy et al., 2002), which then affects values of measured forces.

To measure GG interaction (Fig. 1B, left), cantilever tips and polystyrene Petri dishes were incubated with 2 mg/ml biotinylated BSA (yellow in the figure) at 4°C overnight to minimize non-specific interactions between molecules of interest and the dish surface. After washing three times with PBS, the cantilevers and dishes were incubated with 1 mg/ml streptavidin (blue) for 1 h at room temperature, washed three times with G-buffer (5 mM Tris-HCl pH 8.0, 0.2 mM CaCl₂, 0.2 mM ATP, 0.5 mM DTT) and incubated at 4°C for 1 h with 2 µM biotinylated G-actin (Cytoskeleton, Inc) in G-buffer. 0.00025% biotin was added to the G-actin incubation to achieve the low G-actin coating density required for single-bond measurements.

To measure GF interaction (Fig. 1B, right), the cantilever tips were prepared by the same method as for GG experiments, and the Petri dishes were incubated with F-actin in F-buffer (G-buffer plus 50 mM KCl, 2 mM MgCl₂, 1 mM ATP) at 4°C for 1 h. To prepare F-actin, G-actin and biotinylated G-actin were mixed in a 1:20 ratio to obtain a final concentration of 4 µM G-actin, and then incubated in F-buffer for 15 min at room temperature, and sonicated for 1 min (5 s on and 5 s off) in an ice-water bath. The 15 min incubation/1 min sonication procedure was repeated for two more cycles. After sonicating, F-actin was immediately applied to the Petri dish. F-buffer containing 1 mM ATP and 0.00025% biotin was used as working solution for GG and GF interactions.

To isolate a specific end of F-actin, CAPZ was used to block the barbed end (Caldwell et al., 1989) and TMOD3 used to block the pointed end (Weber et al., 1994). A bacterial expression vector for chicken CAPZ was provided by Dr Takashi Obinata (Chiba University, Chiba, Japan) and used to prepare CAPZ as described by Soeno et al. (1998). A bacterial expression vector for human TMOD3 was provided by Dr Velia Fowler (The Scripps Research Institute, La Jolla, CA, USA) and used to prepare TMOD3 as described by Fischer et al. (2003). CAPZ or TMOD3 were incubated with F-actin for 30 min at room temperature before proceeding with GF interaction experiments.

The cantilever tip mounted on a PZT was brought in contact with the dish surface at a preset x-y location, retracted to 10–30 nm above the surface, held for 0.8 s to allow bond formation, and retracted along the z-direction at a speed of 200 nm/s if a bond was present. We adjusted actin coating density and contact time to keep adhesion frequency around 20% to observe single molecular interaction dominantly (Chesla et al., 1998). Multi-bonds in the clamped phase can be detected at rupturing based on force–time traces. We have excluded these data sets. Fig. 1C shows representative force-scan traces in the presence of an actin-actin bond (Fig. 1C, left) detected from the force–time curves. The x axis represents time and the y axis represents force. Once binding was detected during the retraction, force was applied to it via one of the programming paths: (1) loading a given force by a linear ramp and holding at that constant force until the bond ruptures to measure bond lifetime (Fig. 1C, left), (2) loading the bond to 10–27 pN forces and then reducing the force to 5–10 pN to measure bond lifetime (Fig. 1C, middle; peak force preconditioning), (3) loading 1.5-, 2.5- or 3.5-cycles with a 10 pN peak force and holding at 10 pN to measure bond lifetime (Fig. 1C, right shows 1.5-cycle). The maximum lifetime to measure was set at 50 s. The range of forces loaded on actin bonds (3–30 pN) can be resisted by a single F-actin (Shimozawa and Ishiwata, 2009; Lee et al., 2013).

Where t is time, k_i is the off-rate of the i^th state, and w_i is the fraction of i^th state. The sum of w_i equals to 1. The extra sum-of-squares F-test was used to determine the best-fitted dissociation model among first-order, two-state (n=2) and three-state (n=3) models. The parameters were obtained by fitting the lifetime distributions measured from AFM experiments.

We thank Dr Cho-Yin Lee for discussion.